SSC CGL 2027 Ratio and Proportion Word Problems

Ratio and proportion is an important topic in Quantitative Aptitude for SSC CGL preparation. Questions from this chapter may involve dividing amounts, comparing quantities, ages, salaries, mixtures, and changes in ratios. A clear understanding of the basic concepts and formulas can help candidates solve these problems accurately.

In this guide, you will learn the meaning of ratios and proportions, important formulas, shortcut methods, solved examples, and practice questions. These concepts can help you strengthen your arithmetic foundation and prepare systematically for SSC CGL 2027.

1. What Is a Ratio?

A ratio compares two quantities of the same kind. It shows how much one quantity represents in relation to another. A ratio is commonly written as a:b or a/b, where b is not zero.

For example, if a class has 20 boys and 15 girls, the ratio of boys to girls is 20:15. Dividing both terms by 5 gives the simplified ratio 4:3.

Important points:

• Convert quantities into the same units before comparing them.
• Simplify a ratio by dividing both terms by their common factor.
• Keep the order of the quantities consistent with the question.
• Equivalent ratios represent the same relationship.

2. What Is Proportion?

Proportion indicates that two ratios are equal. For example, 2:3 and 8:12 are equivalent because both simplify to 2:3.

If a:b = c:d, then:

The second relationship is called the cross-multiplication rule. It is useful for finding an unknown value in a proportion.

Example: If 3:5 = x:20, find x.

Using cross multiplication:

3 × 20 = 5 × x

60 = 5x

x = 12

Answer: 12.

3. Dividing an Amount in a Given Ratio

When an amount is divided between two or more people in a specified ratio, first calculate the total number of parts. Then divide the total amount according to those parts.

Solved Example 1: Dividing Money

Question: Divide ₹1,200 between A and B in the ratio 2:3.

Solution:

Total parts = 2 + 3 = 5.

A's share = ₹1,200 × 2/5 = ₹480.

B's share = ₹1,200 × 3/5 = ₹720.

Answer: A receives ₹480 and B receives ₹720.

Solved Example 2: Three-Person Ratio

Question: Divide ₹3,600 among A, B and C in the ratio 2:3:4.

Solution:

Total parts = 2 + 3 + 4 = 9.

A's share = ₹3,600 × 2/9 = ₹800.

B's share = ₹3,600 × 3/9 = ₹1,200.

C's share = ₹3,600 × 4/9 = ₹1,600.

Answer: ₹800, ₹1,200 and ₹1,600 respectively.

4. Ratio Problems Based on Ages

Age-related ratio questions usually compare the present ages of two or more people. The key is to represent their ages using a common multiplier and then apply the information given in the question.

Solved Example 3: Present Ages

Question: The present ages of A and B are in the ratio 3:5. If their total age is 40 years, find their ages.

Solution:

Let their ages be 3x and 5x.

3x + 5x = 40

8x = 40, so x = 5.

A's age = 3 × 5 = 15 years.

B's age = 5 × 5 = 25 years.

Answer: 15 years and 25 years.

Solved Example 4: Age Difference

Question: The ages of two people are in the ratio 4:7. If the difference between their ages is 15 years, find their ages.

Solution:

Let their ages be 4x and 7x.

Difference = 7x − 4x = 15.

3x = 15, so x = 5.

The ages are 20 years and 35 years.

Answer: 20 years and 35 years.

Tip: When a question involves ages after a certain number of years, add that number to each person's present age before forming the new ratio. For ages a number of years ago, subtract it instead.

5. Ratio Changes When Quantities Increase or Decrease

Some questions provide an initial ratio and then change one or both quantities. In these cases, express the original quantities using a common variable and apply the stated change before calculating the new ratio.

Solved Example 5: Increase in One Quantity

Question: The ratio of A's and B's amounts is 3:4. If A receives ₹20 more, their amounts become equal. Find their original amounts.

Solution:

Let the original amounts be 3x and 4x.

Since A receives ₹20 more:

3x + 20 = 4x

x = 20.

A's original amount = ₹60.

B's original amount = ₹80.

Answer: ₹60 and ₹80.

6. Direct and Inverse Proportion

Direct Proportion

Two quantities are in direct proportion when they increase or decrease together in the same ratio, assuming other conditions remain unchanged.

For example, if 5 notebooks cost ₹100, then 10 notebooks at the same unit price cost ₹200.

Formula: x₁/y₁ = x₂/y₂ for directly proportional quantities.

Solved Example 6: Direct Proportion

Question: If 8 pens cost ₹120, what is the cost of 12 pens at the same rate?

Solution:

Cost of one pen = ₹120 ÷ 8 = ₹15.

Cost of 12 pens = 12 × ₹15 = ₹180.

Answer: ₹180.

Inverse Proportion

Two quantities are inversely proportional when an increase in one quantity results in a proportional decrease in the other, assuming the relevant conditions remain unchanged.

For example, if the same work is completed by more workers working at the same rate, the required time decreases.

Formula: x₁ × y₁ = x₂ × y₂ for inversely proportional quantities.

Solved Example 7: Inverse Proportion

Question: Six workers can complete a task in 12 days. How many days will 8 workers take if all workers work at the same rate?

Solution:

Workers × Days = Constant.

6 × 12 = 8 × x

72 = 8x, so x = 9.

Answer: 9 days.

7. Important Shortcuts and Exam Tips

• Use variables: Represent quantities in the form ax and bx when their ratio is known.
• Find total parts: Add all ratio terms before dividing a total amount.
• Use cross multiplication: This helps solve unknown values in equivalent ratios.
• Check units: Convert units before comparing lengths, time or other measurements.
• Identify the relationship: Determine whether the question involves direct or inverse proportion.
• Verify the answer: Substitute the calculated values into the original conditions.

8. Common Mistakes to Avoid

1. Reversing the order of the quantities in a ratio.
2. Dividing a total amount without adding all the ratio terms.
3. Using direct proportion in a situation that requires inverse proportion.
4. Forgetting to add or subtract years in age-based questions.
5. Comparing quantities that have different units without converting them first.

9. Practice Questions for SSC CGL 2027

Try these questions before checking the answer key.

Answer Key with Explanations

1. C) ₹1,400: Total parts = 5 + 7 = 12. B's share = ₹2,400 × 7/12 = ₹1,400.

2. B) 20: Total parts = 4 + 9 = 13. One part = 65/13 = 5. Smaller number = 4 × 5 = 20.

3. C) 27 years: Total parts = 2 + 3 = 5. One part = 45/5 = 9. B's age = 3 × 9 = 27 years.

4. C) ₹250: One notebook costs ₹150/6 = ₹25. Ten notebooks cost ₹250.

5. C) 30 days: Workers × Days = Constant. 10 × 15 = 5 × x, so x = 30 days.

10. How to Prepare Ratio and Proportion

Begin with simple ratio simplification and equivalent ratios. Next, practise dividing amounts, age problems and questions involving changes in quantities. Once these concepts are clear, move on to direct and inverse proportion word problems.

Maintain a formula notebook, solve short practice sets regularly and review incorrect answers. Focus on understanding the relationship between the quantities instead of memorising a different trick for every question.

Check the official SSC CGL notification and syllabus when released for the applicable 2027 examination details. This article is a preparation resource and does not guarantee that a particular question will appear in the examination.

Frequently Asked Questions

1. What is the basic formula for proportion?

If a:b = c:d, then a × d = b × c, provided the ratios are defined.

2. How do you divide an amount in a ratio?

Add the ratio terms, divide the total amount by the sum of the terms, and multiply by each person's ratio term.

3. What is the difference between direct and inverse proportion?

In direct proportion, both quantities change in the same direction. In inverse proportion, one increases as the other decreases under the stated conditions.

4. How are age-ratio questions solved?

Represent the ages using a common variable, apply the given sum or difference, and solve for the variable.

5. How can I improve my speed in ratio questions?

Practise simplifying ratios, calculating total parts and identifying direct or inverse relationships. Review mistakes after each practice set.